REMARKS ON A QUANTUM STATE EXTENSION PROBLEM

The problem is considered of finding, for a given pair of states on C*-algebras A1 ⊗ A2 and A2 ⊗ A3, a joint extension to A1 ⊗ A2 ⊗ A3. The fact that, in contrast to classical probability, such an extension may fail to exist, is related to the fact that different convex decompositions of the same quantum state need not have a common refinement. Improved necessary criteria for extensibility in terms of Bell's inequalities are derived, and are compared to the necessary and sufficient criteria, as well as to entropic bounds in the simplest case. © 1990 Kluwer Academic Publishers.